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The family of quaternionic quasi-unitary (or quaternionic unitaryCayley--Klein algebras) is described in a unified setting. This family includesthe simple algebras sp(N+1) and sp(p,q) in the Cartan series C_{N+1}, as wellas many non-semisimple real Lie algebras which can be obtained from thesesimple algebras by particular contractions. The algebras in this family arerealized here in relation with the groups of isometries of quaternionichermitian spaces of constant holomorphic curvature. This common frameworkallows to perform the study of many properties for all these Lie algebrassimultaneously. In this paper the central extensions for all quasi-simple Liealgebras of the quaternionic unitary Cayley--Klein family are completelydetermined in arbitrary dimension. It is shown that the second cohomology groupis trivial for any Lie algebra of this family no matter of its dimension.Comment: 17 pages, LaTe

The family of quaternionic quasi-unitary Lie algebras and their central extensions